Slope Fields

Key Questions

• How do you draw slope fields?

  Example:

  How do you draw the slope field for #dy/dx = x - y#?

  The slope field is a cartesian grid where you draw lines in various directions to represent the slopes of the tangents to the solution. Therefore by drawing a curve through consecutive slope lines, you can find a solution to the differential equation.

  Take the example of #dy/dx# at #(3, 4)#. Here we see that

  #dy/dx = 3 - 4 =-1#

  So you would draw a line of slope #-1# at #(3,4)#. Repeat this for maybe 4 by 4 points to get the following slope field

  

  Hopefully this helps!

  Noah G · 1 · May 10 2018
• How do you draw the slope field of the differential equation #dy/dx=1/2(4-y)(y-2)^(4/3)# ?

  If you are allowed to use a software, then a software called GeoGebra gives us the slope field below.

  

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  I hope that this was helpful.

  Wataru · 1 · Nov 1 2014
• What are slope fields used for?

  Slope field can be used to visualize the flow of the solution curves of its corresponding differential equation. At each point of the solution curve, the curve will have the slope indicated in the slope field.

  Wataru · · Sep 21 2014

• How do slope fields work?
• How do you draw slope fields?
• What are slope fields used for?
• What do slope fields represent?
• What is a slope field of a differential equation?
• How do you draw the slope field of the differential equation #y'=(y^2-y-2)(1-y^2)# ?
• How do you draw the slope field of the differential equation #y'=y-x# ?
• How do you draw the slope field of the differential equation #dy/dx=x/4(3-y)# ?
• How do you draw the slope field of the differential equation #dy/dx=1/3(y-1)^(1/3)# ?
• How do you draw the slope field of the differential equation #dy/dx=1/2(4-y)(y-2)^(4/3)# ?
• How do you sketch the slope field for the differential equation #1/2 x +y -1#?
• How do you sketch a slope field for #dy/dx = (x + 1)^2/y#?